Addendum to matroid tree-width
نویسندگان
چکیده
منابع مشابه
Addendum to matroid tree-width
Abstract. Hliněný and Whittle have shown that the traditional treewidth notion of a graph can be defined without an explicit reference to vertices, and that it can be naturally extended to all matroids. Unfortunately their original paper Matroid tree-width, European J. Combin. 27 (2006), 1117–1128, as pointed out by Isolde Adler in 2007, contained some incorrect arguments. It is the purpose of ...
متن کاملMatroid tree-width
We show that the tree-width of a graph can be defined without reference to graph vertices, and hence the notion of tree-width can be naturally extended to matroids. (This extension was inspired by an original unpublished idea of Jim Geelen.) We prove that the tree-width of a graphic matroid is equal to that of its underlying graph. Furthermore, we extend the well-known relation between the bran...
متن کاملMatroid 3-connectivity and branch width
We prove that, for each nonnegative integer k and each matroid N , if M is a 3-connected matroid containing N as a minor, and the the branch width of M is sufficiently large, then there is a k-element set X ⊆ E(M) such that one of M \X and M/X is 3-connected and contains N as a minor.
متن کاملA Parametrized Algorithm for Matroid Branch-Width
Branch-width is a structural parameter very closely related to tree-width, but branch-width has an immediate generalization from graphs to matroids. We present an algorithm that, for a given matroid M of bounded branch-width t which is represented over a finite field, finds a branch decomposition of M of width at most 3t in cubic time. Then we show that the branch-width of M is a uniformly fixe...
متن کاملBounding connected tree-width
Diestel and Müller showed that the connected tree-width of a graph G, i. e., the minimum width of any tree-decomposition with connected parts, can be bounded in terms of the tree-width of G and the largest length of a geodesic cycle in G. We improve their bound to one that is of correct order of magnitude. Finally, we construct a graph whose connected tree-width exceeds the connected order of a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2009
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2008.09.028